Pythagorean Identity

$\sin^2(x) + 2\cos(x) - 2 = 0$

$\sin^2(x) + 2\cos(x) - \sin^2(x)-\cos^2(x)-1 = 0$

$2\cos(x) -\cos^2(x)-1 = 0$

$\cos^2(x)-2\cos(x)+1 = 0$

$(cos(x) -1)^2 = 0$

$cos(x)=\boxed{1}$